550.111 Statistical Analysis I  Spring 2007
Midterm #3 version A solution/sketch
1.
Suppose a random sample of size
n
measurements is taken from a normally distributed population
with unknown mean
μ
and unknown standard deviation
σ
.
The sample mean and sample standard
deviation are
x
n
= 110 and
s
= 20, respectively. The following are separate question unless otherwise
noted.
(a) If
n
= 225, construct an approximate 95% confidence interval for the population mean
μ
, and then
interpret the meaning of this interval.
Since
n
= 225 is large, an approximate 95% confidence interval is given by
x
n
±
z
.
025
s
√
n
. Plugging
in the data values given we find the 95% confidence interval to be 110
±
1
.
96
20
√
225
= 110
±
1
.
96
20
15
=
(107
.
4
,
112
.
6).
(b) If
n
= 7, construct a 95% confidence interval for the population mean
μ
.
Since
n
= 7 is small. a 95% confidence interval is given by
x
n
±
t
.
025
(6)
s
√
n
. Therefore, our 95%
confidence interval is given by 110
±
2
.
447
20
√
7
= (91
.
5
,
128
.
5).
2.
A statistics professor wishes to test if the mean student exam scores on a standardized statistics
test differs from that of the national average of 76. Of the 120 students taking this exam it was found
that the sample mean exam score was 79 with a sample standard deviation of 12.
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 Spring '10
 Jooe
 Statistics, Null hypothesis, researcher, Tupperware Corporation

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